Question

The angles of a quadrilateral are in the ratio of 1:2:3:4. What is the measure
of the four angles?

Answer 1

Answer:

36, 72, 108, and 144.

Step-by-step explanation:

As the ratio is 1 : 2 : 3 : 4, let the angles are a, 2a, 3a and 4a.

  We know, sum of all angles in a quadrilateral is 360:

⇒ sum of all angles = 360

⇒ a + 2a + 3a + 4a = 360

⇒ 10a = 360

⇒ a = 360/10

⇒ a = 36

  Hence,

angles are :a = 36

     2a = 2(36) = 72

     3a = 3(36) = 108

     4a = 4(36) = 144

Answer 2

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Question

• The angles of a quadrilateral are in the ratio of 1:2:3:4. What is the measure of the four angles?

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Given:-

• Ratio of angles 1:2:3:4

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To Find :-

• Measure of all four angles.

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Solution :-

• In Quadrilateral the sum of all four angles is 360°

Let,

the ratio of first angle be X.

the ratio of second angle be 2x.

the ratio of third angle be 3x.

the ratio of fourth angle be 4x.

Now,

Sum of all four angles in quadrilateral=360°

• x +2x +3x +4x =360°
• 10x= 360°
• x= 360/10
• x= 36°

∴ The 1st angle of quadrilateral is 36°

∴ The 2nd angle of quadrilateral is 2×36=72°

∴ The third angle of quadrilateral is 3×36=108°

∴ The fourth angle of quadrilateral is 4×36=144°